A federal judge said on Tuesday the U.S. government appeared on track to reunite by a Thursday deadline most of the families separated at the U.S.-Mexican border as part of the Trump Administration's "zero tolerance" toward illegal immigration.

The judge, however, put off deciding on a petition by civil rights groups to postpone deporting any of the parents for seven days after they get their children back. A temporary order currently bars deportations of the families until the matter is resolved.

U.S. District Judge Dana Sabraw, who last month gave federal immigration officials until Thursday to return some 2,500 children to their parents, commended them on Tuesday for the "remarkable achievement" of having largely accomplished that task.

In late June, President Donald Trump ended the practice of splitting up families after audio and video of children wailing and sitting in cages sparked international outrage.

As of Monday, at least 879 parents had been reunited with their children, according to a joint court filing by the government and the American Civil Liberties Union.

Another 463 parents were no longer in the United States but their children were here, and it was unclear when those families would be reunited. The government could not say whether they were deported or left voluntarily.

Children under five were reunited with their parents earlier this month, although the government missed a court-ordered deadline for doing so.

The reunification process has been marred by disarray within state and federal government agencies and difficulty tracking adults and children in detention.

Judge Sabraw postponed until Friday ruling on a motion by the ACLU asking that deportations be delayed.

The ACLU said in court papers that the time was necessary for the parents to consider legal options for their children, who might be better off remaining in the United States to pursue asylum. Most of the parents fled violence in Guatemala, Honduras and El Salvador.

Parents with a final order of removal already get 48 hours to decide if they want to be reunified and return home as a family, or leave their child in the United States, the government said in a court filing on Tuesday.

The government also said that Sabraw lacked the authority to block the government from carrying out removal orders.

Sabraw said he needed additional information on the status of parents and children awaiting deportation before ruling.

The issue sparked a sharp exchange between attorneys for the two sides, with an ACLU lawyer claiming that the extra time was needed in part because "things on the ground are a mess."

Scott Stewart, an attorney for the U.S. Department of Justice, said that government attorneys had worked hard to comply with the court's orders, and "we have many reasons to be proud."